The invention is in the field of nuclear magnetic resonance (NMR) and more particularly relates to NMR probes capable of generating an RF magnetic field along the axis of a sample oriented at a selected angle with respect to a polarizing field.
It is a standard procedure of analysis by magnetic resonance to rotate a sample at a high rate in a uniform magnetic field to obtain an improved average homogeneous sample volume. It is also characteristic of certain specific experiments to orient the rotational axis at a selected angle with respect to the polarizing (B0) field. The selected angle is most frequently the angle corresponding to the zero of the function 3 cos 2xcex8xe2x88x921. This angular dependence is found in the chemical shift anisotropy and the dipolar coupling of nuclei. This angle, corresponding to 54xc2x0 44xe2x80x3, (the xe2x80x9cmagic anglexe2x80x9d) greatly simplifies NMR spectra of solids.
In order to achieve the desired RF magnetic field (B1) distribution over the volume of the sample, an appropriate RF current distribution is to be prescribed in the neighborhood of the sample. The practical implementation is a surface current distribution defined on the surface of a cylinder 10 containing the sample with cylindrical axis at the desired (magic) angle. This cylinder 10 represents a former on which conductors are situated and within which the sample is contained. FIG. 1 is an explanation of the geometry of the present apparatus in the context of an NMR magic angle spinning experiment. It will be apparent that the invention is not restricted to the NMR context. The field B0 is, in the NMR context, the polarizing field. It should be regarded as defining a particular direction in space. A coordinate system based upon a selected axis Z is at some angle from B0. In the NMR context Z is a rotational axis for sample spinning and it is, in practical arrangements, the axis of a cylindrical former 10 upon which coil windings 11, 12 are supported. The windings 11, 12 must generate a magnetic field B1 in a direction orthogonal to B0 Consider B0 as the normal to a plane containing B1.
The prior art sought to realize the desired B1 field strength in the geometry of FIG. 1 with a solenoidal coil, coaxially wound about the coil former on the desired spinning axis, with coil loops tilted to define planes (approximately) which form an angle "psgr" with respect to the spinning axis, where "psgr" is the complement (≈35xc2x0) of the magic angle (54.7xc2x0). The prior art idealized this arrangement for computational purposes as an approximation to a set of current loops, each lying in a plane defining a normal at the desired angle, the several planes aligned along the z axis of revolution. FIG. 2 shows the tilted current loops of the prior art in the context of a typical magic angle experimental arrangement. This prior art is reported by Sun and Maciel, J. Mag. Res. A105, pp. 145-150 (1993).
For a standard solenoid the magnetic field distribution is found from the Biot-Savart equation as induced by a number of circular current loops aligned on the z axis and producing a magnetic field which is aligned along the z axis. A real solenoid has some finite pitch, finite length and discrete windings with finite dimensions and substantial spacing, with resulting non-zero field components other than the axial component. Apart from these minor effects, the prior art exhibits further departures from an axial field as an inherency of the prior art approach. Consider that a (closely wound) cylindrical solenoid may be regarded as a number of circular current loops. The tilting of a current loop prescribes a plane intersecting the cylinder at the tilt angle and thereby defining an ellipse of corresponding eccentricity. The result of an elliptical current loop is to generate radial and azimuthal magnetic field components in addition to the axial component. Thus, the efficiency of the coil, as determined by the energy required to produce a desired B1 amplitude and distribution and to sustain that B1 over a desired pulse width, will require significantly more RF power than would be the case if these non-axial components could be reduced or eliminated.
In order to obtain a magnetic field substantially confined to a desired acute orientation with respect to the axis of a cylinder of revolution on which suitable windings are disposed, that field is prescribed and solutions are obtained for a surface current distribution on that surface of revolution which yields the desired magnetic field over the axial extent of the windings. The resulting contour function is then approximated by a discrete distribution of the integrated current density that yields the desired oriented field with substantially vanishing components orthogonal to the desired direction. In one embodiment the contours are broken and adjacent contours joined to produce a serial assembly of current loops that generate the desired field. In another embodiment a parallel assembly of current loops is obtained.